The new curriculum standard is here, can I still learn mathematics by brushing the questions? Experts from the Ministry of Education responded

　　The new curriculum standard is here, can I still learn mathematics by solving problems?

Mathematics is always one of the subjects that parents and teachers attach the most importance to as the subject "the most distinguishable subject".

It is the "most important" in the extracurricular training classes, and it is a must in various selection examinations.

In the early years, the vigorous "Olympic Mathematics Class" was a lively event. To this day, "Mathematics homework photos can detect correct answers" is still the biggest selling point of all extracurricular tutoring software.

The mathematics curriculum reform affects the whole body, and every change in it has attracted much attention.

With the gradual advancement of the new college entrance examination and the abolition of the division of liberal arts and sciences, in June this year, the new curriculum standards for high school mathematics were promulgated.

Therefore, what challenges do teachers face in teaching and what adjustments should students make in their studies?

The reporter interviewed Wang Shangzhi, a member of the Mathematics Teaching Steering Committee of the Ministry of Education, the deputy leader of the development group and the leader of the revision group of "General High School Mathematics Curriculum Standards".

1. Mathematics, from knowledge to ability, from ability to literacy

As mathematics educators, we must think about what mathematics wants children to learn?

After entering the society, even if some mathematics knowledge is forgotten, what can be left for children?

In the process of formulating and revising the new curriculum standards, we hope that the core qualities left by mathematics to children are: mathematical abstraction, logical reasoning, mathematical modeling, intuitive imagination, mathematical operations, and data analysis.

Reporter: As a witness, can you analyze the several changes that mathematics has experienced?

Many parents reported that after alleviating the pressure of choosing a school and canceling various bonus points and cup competitions, the only thing they dare not give up is mathematics.

If you ask the classmates which training class is the most popular, the answer must be "mathematics". What do you think of this?

Wang Shangzhi:

The guiding ideology for the development of the new curriculum standard is to implement the fundamental task set by the central government for education-Lide and

people.

How to implement this task?

In other words, what does math want children to learn?

After entering the society, what mathematics can leave children, that is the core quality.

At present, in the process of formulating new curriculum standards, we hope to leave children with mathematics literacy in the following six aspects: mathematical abstraction, logical reasoning, mathematical modeling, intuitive imagination, mathematical operations, and data analysis.

　　In fact, this is a question that many countries are thinking about.

From the 20th century to the 21st century, with the development of society and science and technology, the basic skills that students should possess have changed, so we will naturally change accordingly.

For example, there is a survey conclusion that in the 20th century, every person has to experience one or two occupations in his life. In the 21st century, according to data predictions, each person may experience about ten occupations.

　　The skills needed to deal with one profession and multiple professions are different. In social development, the role of mathematics has also changed.

Jiang Boju, an academician of the Chinese Academy of Sciences, has such a statement that "mathematics has moved from behind the scenes to the foreground, directly creating value for society."

Our mathematics education reform took place in this context and experienced three steps.

From taking knowledge as the core, gradually developing to taking competence as the core, and now taking literacy as the core.

　　In the 1960s, the mathematics syllabus revolved around how to learn knowledge.

Later, a group of mathematicians proposed that the goal of mathematics education is to improve the three abilities, namely, mathematical operation ability, logical reasoning ability and spatial imagination ability.

As soon as the three abilities were proposed, they were widely recognized by the mathematics, mathematics education and front-line teachers. Around 2002, we began to develop experimental drafts of high school curriculum standards. Some experts talked about coping with new changes, so the three abilities changed. Five abilities: abstract generalization, computational solution, logical reasoning, spatial imagination, and data processing.

Until today, it has become the six core literacy. Simply put, the literacy is to integrate knowledge and skills, thinking methods, key abilities, emotional attitudes and values, and leave more things for students.

　　What I want to say is that I hope that students can develop and improve in these six areas by learning the knowledge, skills, and thinking methods of mathematics in the atmosphere of mathematics education, so that they can pass education and learn through each subject. , To promote the comprehensive development of students' morality, intelligence, physical education, and art.

　　In the past, knowledge-based education has gradually changed to a "people-oriented" education through this curriculum standard study, and it is proposed that core literacy is also based on the development of students.

　　To put it another way, in the past we focused on learning mathematics, now we should not only learn, but also hope that students will learn mathematics.

　　In addition, one thing is very important.

For all students, the compulsory and optional compulsory content to be studied in mathematics is "less".

Our course structure has changed.

We treat all students equally and no longer divide liberal arts and sciences.

　　We provide a wealth of elective courses for children who are interested in mathematics and capable.

The elective courses are divided into five categories. There are mathematics courses suitable for the development of science, mathematics courses suitable for the development of liberal arts, mathematics courses suitable for sports, music, and fine arts, and mathematics courses suitable for the development of special talents. For example, university elective courses.

The university elective courses have 6 credits and three subjects: calculus, linear algebra and analytic geometry, and probability theory.

　　In short, mathematics is "cutting its branches and strengthening its strengths" to provide suitable education for different children.

2. Is mathematics "simpler"?

The previous mathematics test questions were smart and concise. It would be wrong to miss one word and one more word.

For mathematics test questions, some questions still maintain this style, but will change the "relatively fixed test form". In addition, as the requirements for practice and innovation capabilities increase, some test questions increase the background, mainly examining students’ The ability to solve problems in a more real situation-application ability.

This is the quality of mathematical modeling.

Such test questions require good core mathematics literacy, good reading comprehension ability, and good application ability. We hope teachers and parents will see this trend of change and realize it step by step.

Reporter: Parents are very concerned about which part of the content is missing?

The knowledge to be investigated is less, is the mathematics of the college entrance examination easier?

Wang Shangzhi:

On October 13, 2020, the State Council issued the "Overall Plan for Deepening Educational Evaluation Reform in the New Era", in which Article 20 states: "Steadily advance the reform of the high school and college entrance examination, and build a test content system that guides students' comprehensive development of

, physical education, and labor. . Change the relatively solid test question format, enhance the openness of the test questions, and reduce the phenomenon of rote memorization and mechanical brushing."

　　It turned out to be 16 credits for science and 14 credits for liberal arts.

At present, liberal arts are no longer divided into subjects, and our requirements have been unified into 14 credits.

There are 8 credits for compulsory courses and 6 credits for optional compulsory courses, a total of 14 credits.

　　One credit is equivalent to 18 class hours, which means we have to subtract 36 class hours from it.

These 36 class hours are allocated to other electives, to candidates for music, sports and beauty, and candidates for special talents.

There is another change in the curriculum standards this time, which is to evaluate and guide the college entrance examination questions.

The past curriculum standards mainly addressed the six questions of "what to learn, what to teach, to what extent, how to teach, how to teach and how to learn".

This time, the curriculum standard has increased the academic quality standard, and the problem that the academic quality standard must solve is to guide the proposition of the test, for example, increase the openness of the test questions, which is a big change.

　　In short, students taking the college entrance examination need to understand that learning mathematics cannot be satisfied with memorization and imitation. Although there is less "informative" content to be prepared, the openness of test questions has increased.

Reporter: After the reform, how has the teacher's teaching changed?

How should students' learning be adjusted?

What parents are most concerned about is, do they still need to write questions?

Wang Shangzhi:

Another point in the reform of curriculum standards is to strengthen mathematical modeling and mathematical inquiry activities in content, and use it as a carrier to enhance students' practical and innovative abilities.

　　In fact, the "difficulty" of the title is difficult to express intuitively, because we no longer emphasize "knowledge" but "ability".

For example, in this year's Shandong Province College Entrance Examination Papers, there are about seven or eight questions with application background and specific context.

　　Previously, our mathematics test questions were capable and concise, and the meaning of a word would be wrong.

The current test questions increase the application background, which examines the students' ability to solve problems in more realistic situations.

In this sense, is it useful to brush questions?

There are a lot of changes in the situation, and it is basically impossible to "push on the subject" and "brush the subject".

　　From the perspective of mathematics itself, can traditional routines deal with actual situations?

Can you handle a large number of test questions?

Teachers and students must understand that what we require is that students can solve problems in real situations.

3. Where should the foundation of mathematics be "played"?

In fact, the boundaries of a good math class are somewhat blurred, and it requires students to develop in an all-round way.

"Fast and accurate" is not the most important, but the logical connection between knowledge points is the most important.

Do not divide mathematics into small knowledge points, but build students' logical thinking ability bit by bit from the understanding of the topic.

Reporter: How does the teacher adapt to the change of situation?

How to teach mathematics more efficiently?

Should mathematics be learned in advance?

Wang Shangzhi:

I said a common problem among teachers. Our teachers seldom read the questions seriously when explaining the problem.

This is true even for high-quality courses. When a question comes out, the teacher directly asks the classmates: "Does this question everyone know? See who is quick!" Every time I find it, I ask, why don't you read the question?

　　We always say that mathematics should focus on the foundation and efficiency from textbooks, but many foundations are just not well laid.

Let's take the most classic mathematics problem "chicken and rabbit in the same cage" as an example. This topic will probably be learned in the third grade of elementary school.

General questions will indicate how many chickens and rabbits there are, how many "legs" the two animals have, and ask how many chickens and rabbits there are.

Teachers' explanations are generally like this: Suppose the cages are all chickens or rabbits, and then perform calculations.

I heard some children ask questions, "Why assume this? It is obvious that a rabbit has 4 legs and it is not a chicken. How can it be assumed to be a chicken?" The teacher usually does not explain, but just says, "Write it down, just like that. ".

In this way, the child does not understand, but just remembers it, and if the topic changes, it still won’t.

In this case, you can only "brush the questions".

In this way, the burden on students will be heavy.

　　This is what we most hope teachers make changes, change teaching methods, not "teach knowledge" but "teach ability."

For example, in the "chicken and rabbit in the same cage" problem above, asking students to consider "the number of chicken legs and rabbit front legs" is easier to understand than "assuming that they are all chickens". The difference lies in respecting students' cognitive laws and using them ( Most) The level of understanding is reasonable and the foundation is laid.

After each question comes out, the teacher should read the question first, how to understand the meaning of the question, and think logically.

This is how children’s logical thinking ability is cultivated. Teachers can even ask students to repeat the meaning of this topic. They will naturally understand when they encounter similar problems in the future.

For example, division. Let students understand that division is "equal division", divided into several parts evenly.

For another example, for some multiplications and divisions that contain "0", the teacher clearly knows that the result is still "0", but the steps cannot be omitted. This helps the "digits" not to cause problems.

　　We are talking about attaching importance to the foundation, which is here.

In fact, the boundaries of a good math class are somewhat blurred, and it requires students to develop in an all-round way.

"Fast and accurate" is not the most important, but the logical connection between knowledge points is the most important.

Do not divide mathematics into small knowledge points, but build students' logical thinking ability bit by bit from the understanding of the topic.

　　Mathematics learning is based on certain life experience and understanding ability. In this sense, you must not learn it in advance.

For example, if students don’t accumulate enough Chinese "antonyms" and "synonyms" to learn "positive and negative numbers", they will lack the understanding basis. From "antonyms" to "quantity with opposite meanings" is an improvement, and then combined with "given Set 0 point situation".

For example, the unit of altitude must have a "0 point", which may be above or below.

Then think about the situation that "need to set 0 points", for example, describe the location of the building in the road, step by step, so that students learn to think.

　　Mathematics needs to do questions, but when doing the questions, you must understand the questions. This is called the foundation, and this kind of foundation is the foundation that works.

This is also a new requirement of our curriculum standards. In short, we hope that students will learn and think about problems in order to cope with more changes in the future.

(Our reporter Yao Xiaodan)